document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99836>Question 99836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maria and Jan are running around an indoor track. They leave from the same point but jog in different directions at different constant speeds. Maria can run around the entire track in 40 seconds. She meets Jan every 15 seconds. How long does it take Jan to run arount the entire track ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72841 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> distance(d)=rate(r) times time(t) or d=rt;r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let t=time it takes Jan to run around the entire track<BR>\n" );
document.write( "And let L=length of the track<BR>\n" );
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document.write( "We are told that Maria can run around the track in 40 sec.<BR>\n" );
document.write( "So we know that Maria's rate is d/t=L/40<BR>\n" );
document.write( "The distance Maria travels in 15 sec =rt=(L/40)*15 or 15L/40 or 3L/8 ft\r<BR>\n" );
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document.write( "Together, Jan and Maria can run around the length of the track (L) in 15 sec.  So the distance Jan travels in 15 sec=L-distance Maria travels in 15 sec, or\r<BR>\n" );
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document.write( "The distance Jan travels in 15 sec =L-3L/8=5L/8 ft \r<BR>\n" );
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document.write( "Now we can set up a simple ratio to get to the answer\r<BR>\n" );
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document.write( "5L/8 is to 15 sec as L is to t  or\r<BR>\n" );
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document.write( "(5L/8)/15=L/t  simplifying the left side we get\r<BR>\n" );
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document.write( "L/24=L/t  multiply both sides by 24t<BR>\n" );
document.write( "Lt=24L  divide both sides by L\r<BR>\n" );
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document.write( "t=24 sec--------------------time it takes Jan to run around the track\r<BR>\n" );
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document.write( "Ck<BR>\n" );
document.write( "Jan's rate is L/24<BR>\n" );
document.write( "In 15 sec, Jan runs (L/24)*15 or 15L/24 ft\r<BR>\n" );
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document.write( "Maria's rate is L/40<BR>\n" );
document.write( "In 15 sec, Maria runs (L/40)*15=15L/40\r<BR>\n" );
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document.write( "15L/24+15L/40=L<BR>\n" );
document.write( "3L/8+5L/8=8L/8=L<BR>\n" );
document.write( "L=L\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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